Next, you have to decide whether you will register the domain name yourself or set your web space provider to do it for you. Unless you have a strong reason to do it yourslef, we recommend you to rely on your hosting provider's experience and knowledge. However, make sure that InterNIC records will show your company as the owner of the name.
Many hosting providers will register your domain name without additional charge (all you pay is $70.00 to InterNIC or whatever charge imposed by registrar of particular TLD is).
If you decide to let your provider register your name, you have to send them your company information and specify who is going to be the administrative and billing contact for your domain.
If you wish to do the registration yourself, you need to get NIC Handle for technical contact and at least 2 IPs and DNSs from your provider. Then you can contact the registrar of TLD of your choice and register the domain.
Processing times vary from registrar to registrar.